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We are concerned with the one-dimensional piston problem for the compressibleEuler equations of Chaplygin gas. If the piston moves at constant subsonicspeed to the uniform gas, there exists an integral weak solution for the pistonproblem, consisting of a shock separating constant states ahead of the piston.While if the speed of the piston is sonic or supersonic, a singular measuresolution, with density containing a Dirac measure supported on the piston,shall be introduced to solve the problem. Integral weak solution exists for thepiston receding from the gas with any constant speed, and there is no vacuum.In the extreme case as the Mach number of the piston goes to infinity, thelimiting equations and solutions are the same as that for the polytropic gases.

Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gas